Although the theoretical aspects of the particle swarm optimization (PSO) seem to be forsaken, the few previous modeling studies -even with some assumptions- enlarged our knowledge of the PSO process. Here, we suggest a new model of PSO where all the N particles of the swarm and their components are considered. The iterative process is formulated by a 3Nx3N block triangular matrix and its spectral radius is evaluated and displayed. Besides, the convergence related parametrization criteria are derived. Compared to previous results, a more restrictive acceleration coefficients criterion is found. Simulations are then carried on CEC 2017 benchmark functions using eight PSO variants and show better results when considering the more restrictive criterion.
